OPTICAL ELASTICITY IN OBLIQUE-PRISMATIC CRYSTALS. 433 



taking care not to alter the inclination of T to the index, (this may 

 be effected by moving the crystal, the index being fixed, tiU the image 

 of some well defined object seen by reflexion in T appears in the 

 same direction after the crystal is turned as it did before.) If the 

 index be now turned till the center of the coloured rings coincides 

 with the mark, the angle it has described between the observations 

 will be manifestly equal to twice the angle between the apparent 

 direction of the optic axis in air and a normal to T. The angle 

 between the optic axis in air and a normal to any other known face 

 of the crystal being found in the same manner, the direction of the 

 optic axis in air wiU be completely determined. 



4. To find the optic axes, their apparent directions in air being 

 known. 



Let Qlt, Q'K (Fig. 1.) be tangents to the circular and eUiptic sec- 

 tions of a wave diverging from O made by a plane through the optic 

 axes, and therefore OQ, OQ', perpendiculars to QB, will be the optic 

 axes; OP the direction in which the optic axis OQ is seen in air; 

 OS a perpendicular to the faces through which it is seen. 



The vibrations in that part of the wave which has a circular sec- 

 tion are perpendicular to the plane QOQ, consequently a ray polar- 

 ized in the plane QOQ is refracted in that plane according to the 

 law of sines. Let m be the ratio of the sine of incidence to the sine 

 of refraction for such a ray out of air into the crystal, D the mini- 

 mum division of the ray when refracted in the plane QOQ' through 

 the prism formed by two natural or artificial planes meeting at an 

 angle / in a line perpendicular to QOQ. Then ^ sin ^ / = sin ^ (Z) + /), 

 and fM sin QOS = sin POS. Whence the direction of QO is known. 

 0*0 being found in the same manner, the axes of elasticity O^, Oi[, 

 which bisect the angles qOQ, QOQ, are also known. 



5. The diagram which accompanies the description of each crystal, 

 is the representation of a sphere, to the surface of which the faces of 

 the crystal are referred by means of perpendiculars drawn from the 

 center of the sphere. The point in which the perpendicular to any 



